The global attractivity of the rational difference equation  <IMG WIDTH="171" HEIGHT="59" ALIGN="MIDDLE" BORDER="0" SRC="/proc/2008-136-01/S0002-9939-07-08860-0/gif-title0/img1.gif" ALT="$ y_n=A+left(frac{y_{n-k}}{y_{n-m}}right)^p$">期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The global attractivity of the rational difference equation $y_n=A+left(frac{y_{n-k}}{y_{n-m}}right)^p$

Authors:

Kenneth S. Berenhaut John D. Foley Stevo Stevic

Affiliation:

Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109 ; Department of Mathematics, Wake Forest University, Winston-Salem, North Carolina 27109 ; Mathematical Institute of The Serbian Academy of Science, Knez Mihailova 35/I 11000 Beograd, Serbia

Abstract:

This paper studies the behavior of positive solutions of the recursive equation

$displaystyle y_n=A+left(frac{y_{n-k}}{y_{n-m}}right)^p,quad n=0,1,2,ldots,$

with $y_{-s},y_{-s+1}, ldots, y_{-1} in (0, infty)$ and

, where

. We prove that if

, and

, then

tends to

. This complements several results in the recent literature, including the main result in K. S. Berenhaut, J. D. Foley and S. Stevic, The global attractivity of the rational difference equation $y_{n}=1+frac{y_{n-k}}{y_{n-m}}$ , Proc. Amer. Math. Soc., 135 (2007) 1133-1140.

Keywords:

Rational difference equation stability.

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